SOLUTION: A newspaper finds that the mean number of typos per page is 3. Find the probability that (a) exactly 4 typos are found on a page, (b) at most 4 typos are found on a page, and (c) m

Algebra ->  Probability-and-statistics -> SOLUTION: A newspaper finds that the mean number of typos per page is 3. Find the probability that (a) exactly 4 typos are found on a page, (b) at most 4 typos are found on a page, and (c) m      Log On


   

Question 981948: A newspaper finds that the mean number of typos per page is 3. Find the probability that (a) exactly 4 typos are found on a page, (b) at most 4 typos are found on a page, and (c) more than 4 typos are found on a page.
Answer by mathmate(429) About Me  (Show Source):
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Given:
A newspaper find the mean number of typos per page is 3.
Find probability that
(A) exactly 4 typos are found on a page
(B) at most 4 typos are found on a page
(C) more than 4 typos are found on a page.

Solution:
This is a Poisson distribution with lambda=3.
The Poisson distriibution is
P(n)=lambda%5En%2Ae%5E%28-lambda%29%2Fn%21

(A) n=4
P(4)=lambda%5E4%2Ae%5E%28-lambda%29%2F4%21=0.16803
(B) n<=4
P(n<=4)=P(0)+P(1)+P(2)+P(3)+P(4)
=0.04979+0.14936+0.22404+0.22404+0.16803
=0.81526
(C) n>4
P(n>4)=1-P(n<=4)=1-0.81526
=0.18474